The bilayer 2-dimensional electron gas (2DEG) consists of two closely spaced 2DEGs, between which Coulomb interactions and tunneling effects can lead to new behaviors which are absent in the individual layers ^{[1] [2] [3]} .  In these bilayers, an insulating spacer is necessary to separate the 2DEG layers.  In twisted bilayer graphene, layers can be stacked directly on each other yet still retain a degree of independence.  This independence is possible because of the carbon honeycomb lattice of graphene, which results in weak coupling between layers ^[4] and a circular Fermi surface centered at nonzero K vectors ^[5] .  The latter is key, because a relative twist angle between the graphene bilayer lattices can cause the Fermi surfaces of the layers to not overlap at low densities (Figure 1).  This fact preserves the linear Dirac dispersion in the twisted bilayer graphene ^{[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]} but with twice the number of Dirac cones due to the two layers ^{[1] [3] [6]} .

We measure the magnetoresistance of dual-gated twisted bilayer graphene devices, which exhibit the quantum Hall effect and magnetoresistance oscillations of two monolayer graphene sheets conducting in parallel. As we vary the gate voltages, we observe inter-layer Landau level crossings, allowing us to quantify the layer charge transfer and finite screening effects between the layers. This incomplete screening of the applied field, due to graphene’s small density of states and the close spacing between the layers, lets us extract the inter-layer capacitance of the atomically-spaced graphene sheets. At high magnetic fields, we observe a pattern of insulating states centered at zero density originating from layer-polarized edge modes.

Figure 1: Magnetoresistance studies of twisted bilayer graphene. (a) Lattice structure. (b) Twist angle separates the Fermi surface of each layer in K-space. (c) Device schematic (d) Magnetoresistance as a function of filling factor ν_tot and displacement field at B=4Tesla. Peaks in magnetoresistance are due to Landau levels. Landau levels of each layer move in different directions with displacement field. (e) Insulating states due to electron-electron interactions develop in twisted bilayers at very high magnetic field, which varies with filling factor and displacement field.

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